The Problem of the Limitations of the Educational Model Experiment on

Population Genetics and Its Solution

Elena V. Komarova

1 a

and Arnold E. Kiv

2 b

Immanuel Kant Baltic Federal University, 14 Aleksandra Nevskogo Str., Kaliningrad, 236041, Russia

Ben-Gurion University of the Negev, P.O.B. 653, Beer Sheva, 8410501, Israel

Keywords:

Population Genetics, Repeatability of the Experiment, Massiveness of the Experiment, Ideal Population,

Hardy-Weinberg’s Law.

Abstract:

The difﬁculty of conducting an educational model experiment on population genetics is in meeting the re-

quirements of mass and replication. The evolution of a model experiment to study the Hardy-Weinberg law

according to the methods proposed by the authors is considered – from the use of material models and man-

ual counting of alleles and genotypes to the transition to automatic random distribution of elements of the

genotypic structure of the population and automatic calculation of the resulting indicators. The technique of

fully automated modeling of the genetic structure of the population allows to increase the size of the model

sample by orders of magnitude. When using the technique in group work of students, it becomes possible to

demonstrate the essence and differences of technical and biological replication as requirements for organizing

a biological experiment. The technique is currently developed to work only with very large ideal populations.

1 INTRODUCTION

The academic subject “Biology” is a didactically

adapted system of scientiﬁc biological knowledge. In

the natural sciences, and biology is undoubtedly one

of them, experiment is one of the main methods of

research (Nechypurenko et al., 2021). This is what

makes it possible, on the basis of the various factual

material obtained, to make broad generalizations, to

proceed to the establishment of connections, patterns

that allow deeper penetration into the essence of the

phenomena under study. Much has already been said

about the experiment in biological science, about its

types, methods, requirements for organization, limi-

tations and difﬁculties of application. A huge number

of scientiﬁc works are devoted to the history of the

experimental method in biology. However, we were

and are interested at the moment in the experimental

method from the point of view of the possibilities of

its use in biological education. In addition, narrow-

ing down the subject area of interest to us, it is worth

noting that the model experiment occupies a special

place in high school. This allows you to create models

of real objects and prototype the processes that occur

https://orcid.org/0000-0002-3476-3351

https://orcid.org/0000-0002-0991-2343

with them in reality. In previous works, the authors

has covered some aspects of this issue (Komarova and

Azaryan, 2018; Komarova and Starova, 2020).

Modern course of biology in high school is based

on the fundamental theoretical generalizations of ba-

sic biological science – scientiﬁc theories and laws.

Fundamental genetic laws, classically studied by high

school students, are laws of heredity of Mendel.

Given the trends of development of modern biolog-

ical sciences, namely, the development of theoretical

biology, the main issues which are problems of ge-

netics, ecology, evolution, law of genetic equilibrium

concentrations (the law of Hardy-Weinberg) is con-

sidered as a fundamental law, the disclosure of which

to high school students is aimed at understanding by

them of the mechanism of evolution in general. This

law reveals the regularities of functioning of living at

the population – species level, including time frames.

Students’ mastering of the patterns of popula-

tion genetics and associated evolutionary theory is

one of the most complex issues in biology course

in high school. Studies (Hammersmith and Mertens,

1990; Mertens, 1992; Moore, 1994; Maret and Riss-

ing, 1998; Mukhopadhyay et al., 2014; Pongsophon

et al., 2007) conﬁrm this.

We have conducted a survey among 52 high

school students to ascertain their level of knowledge

272

Komarova, E. and Kiv, A.

The Problem of the Limitations of the Educational Model Experiment on Population Genetics and Its Solution.

DOI: 10.5220/0010923700003364

In Proceedings of the 1st Symposium on Advances in Educational Technology (AET 2020) - Volume 1, pages 272-286

ISBN: 978-989-758-558-6

about the essence of law of genetic equilibrium con-

centrations, its value for the understanding of the fac-

tors and directions of the evolutionary process.

The tasks were as following:

1. Specify the mathematical equation of the law of

Hardy–Weinberg (multiple answers are allowed):

(a) p +q = 1;

(b) (p + q)

= 1;

+ 2pq + q

= 1;

(d) p

+ pq + q

= 1;

(e) p +2pq + q = 1.

2. Specify an equation describing the genotypic

structure of the population (multiple answers are

allowed): (see the answers to the assignment 1).

3. Specify the equation describing allelic population

structure: (see answers to the assignment 1).

4. What are the conditions of validity of the law of

equilibrium gene concentrations. Students were

asked to solve three problems for the application

of the law of equilibrium of gene concentrations.

The results of the survey are presented in ﬁg-

ures 1–3.

Conditions of validity of the law, according to the

student, were as following: population sizes are large

– 29% of respondents, mating occurs at random –

24%, new mutations do not occur – 18%, all geno-

types are equally fertile – 12%, generations do not

overlap – 12%, there is no exchange of genes with

other populations – 18%, the genes are in the auto-

somes and not in sex chromosomes - 18%, individuals

of different genotypes are equally viable – 12%.

The obtained results allow to formulate the fol-

lowing conclusions: students insufﬁciently under-

stood the description of the essence of the law of

Hardy-Weinberg with two equations, namely, the def-

inition of allelic and genotype structure of the popu-

lation; the students are confused about variables in-

cluded in the equations; knowledge about the condi-

tions of the law is fragmentary. None of the respon-

dents began to address two of the proposed problems,

three of the respondents solved the third task incor-

rectly.

The results of the survey suggest the presence of

formalism in high school students’ knowledge about

the law of genetic equilibrium concentrations. For-

mal approach to training lies in the mechanical mem-

orization of educational material without enough un-

derstanding of its content. The low level of develop-

ment of knowledge about the law of genetic equilib-

rium concentrations is one of the reasons for the dif-

ﬁculties of the students in understanding of the evo-

lutionary content for the understanding of population

genetics and population human genetics in particular.

Simulation, particularly computer simulation is

one of the most effective training methods for demon-

strating to students of the essence of complex biologi-

cal processes, including genetic and evolutionary pro-

cesses in natural populations.

In the process of studying the topic of the dis-

play of experimental method at the level of school

biological education, transformation of ideas about

how it is possible to implement the experimentation

with complex biological systems, including those in-

accessible to the student for direct study, we initially

started out from the following. An educational bi-

ological experiment should maximally meet the re-

quirements that are put forward for scientiﬁc biologi-

cal experimentation. These, in particular, are the reli-

ability in essence, the rule of single difference, repli-

cation, mass nature. From the mid-XXth century, a

lot of attention has been paid to the organization of a

school biological experiment, moreover to its various

types, differing both in the object of research (botan-

ical, zoological, physiological tests, functional tests,

etc.), and in the form of carrying out under the con-

ditions of school laboratory, class (demonstrational,

laboratorial, mental) (Binas et al., 1990; Voronin and

Mash, 1983; Shamrai and Zadorozhnyi, 2003; Frolov,

2007; Brunovt et al., 1973; Bazykin, 1988; Borodin,

1987; Bulaeva, 1977; Sidorova, 2009). Regardless of

the type and form of carrying out, all various types

of educational biological experiment must meet the

abovementioned requirements in order that the results

obtained were maximum consistent.

The biggest difﬁculties in the educational process

are caused by the observance of such requirements as

replication and mass nature. In other words, to en-

sure the veracity of results, the educational experi-

ment should be conducted several times using a sufﬁ-

ciently large number of objects.

It is difﬁcult to implement both the ﬁrst and the

second condition in the educational process due to the

following reasons:

• ﬁrstly, the temporal limitations of the educational

process;

• secondly, due to the inaccessibility of objects for

study in the required quantity;

• thirdly, in the principle of inaccessibility of some

objects and processes for direct study, primarily

due to their objective speciﬁcity: either too small

(organic molecules, cells, viral particles), or too

large (populations).

Let’s turn our attention to these reasons, possible

ways of their elimination.

The Problem of the Limitations of the Educational Model Experiment on Population Genetics and Its Solution

273

We have conducted a survey among 52 high school students to ascertain their level of knowledge about the

essence of law of genetic equilibrium concentrations, its value for the understanding of the factors and directions of the

evolutionary process.

The tasks were as following:

1. Specify the mathematical equation of the law of Hardy–Weinberg (multiple answers are allowed):

A) p + q = 1;

B) (p + q)

= 1;

C) p2 + 2pq + q

= 1;

D) p2 + pq + q

= 1;

E) p + 2pq + q = 1.

2. Specify an equation describing the genotypic structure of the population (multiple answers are allowed): (see

the answers to the assignment 1).

3. Specify the equation describing allelic population structure: (see answers to the assignment 1).

4. What are the conditions of validity of the law of equilibrium gene concentrations. Students were asked to

solve three problems for the application of the law of equilibrium of gene concentrations.

The results of the survey are presented in Fig. 1–3.

Fig. 1. The results of the response to the first task

Fig. 2. The results of the response to the second task

Fig. 3. The results of the response to the third task

Figure 1: The results of the response to the ﬁrst task.

We have conducted a survey among 52 high school students to ascertain their level of knowledge about the

essence of law of genetic equilibrium concentrations, its value for the understanding of the factors and directions of the

evolutionary process.

The tasks were as following:

1. Specify the mathematical equation of the law of Hardy–Weinberg (multiple answers are allowed):

A) p + q = 1;

B) (p + q)

= 1;

C) p2 + 2pq + q

= 1;

D) p2 + pq + q

= 1;

E) p + 2pq + q = 1.

2. Specify an equation describing the genotypic structure of the population (multiple answers are allowed): (see

the answers to the assignment 1).

3. Specify the equation describing allelic population structure: (see answers to the assignment 1).

4. What are the conditions of validity of the law of equilibrium gene concentrations. Students were asked to

solve three problems for the application of the law of equilibrium of gene concentrations.

The results of the survey are presented in Fig. 1–3.

Fig. 1. The results of the response to the first task

Fig. 2. The results of the response to the second task

Fig. 3. The results of the response to the third task

Figure 2: The results of the response to the second task.

Analysis of scientiﬁc literature in regards to the

experimentation in biology showed that since the end

of the 1980s, one of the actively discussed problems

became the problem of pseudoreplication in ecolog-

ical and biological research. In the classical varia-

tion, from the moment of publication of the ﬁrst pa-

per on this topic, pseudoreplication was considered

as a negative experimental practice (Hurlbert, 1984).

Even now, one of the criteria by which reviewers eval-

uate the submitted paper for a journal indexed in the

authoritative international scientometric Scopus and

Web of Science databases is the true and pseudorepli-

cation of the experiments conducted (Brygadyrenko,

2017). Please note that at the moment the scien-

tiﬁc community is still not so categorical in regards

to pseudoreplication of experimental research. Dis-

cussions are being conducted on the issue of reality

and contrivedness of the problem (Rosenberg, 2019;

Kozlov and Hulbert, 2006; Rosenberg and Gelashvili,

2008).

We proceed from the assumption that the biol-

ogy teaching methods cannot stay on the sidelines of

the problems actively discussed in biological science.

Moreover, this question lies in the plane of the science

methodology. The mastery of methodological knowl-

edge and the ability to apply them is the basis for the

formation of a system of biological knowledge for se-

nior high school students. The author’s early works

were devoted to this question (Komarova, 2017). So,

we consider the question of to what extent in school

experimentation in biology it is necessary to take into

account the requirements that S. Hurlbert identiﬁed

as the problem of pseudoreplication of experimental

research in science, as deﬁnitively solvable in the di-

rection of their observance. At the same time, given

that the educational subject still differs from the ba-

sic science in that it is a didactically adapted version

of it, it is necessary to achieve a double effect in or-

ganization of a school biological experiment. The

ﬁrst effect is that the results of the educational ex-

periment should be maximum consistent, obtained by

true replication. The second effect is that the use of

true replication should be maximum ergonomical. Er-

gonomic in time, cost and complexity.

The purpose of this article is to demonstrate the

capabilities of a school model experiment in studying

AET 2020 - Symposium on Advances in Educational Technology

274

We have conducted a survey among 52 high school students to ascertain their level of knowledge about the

essence of law of genetic equilibrium concentrations, its value for the understanding of the factors and directions of the

evolutionary process.

The tasks were as following:

1. Specify the mathematical equation of the law of Hardy–Weinberg (multiple answers are allowed):

A) p + q = 1;

B) (p + q)

= 1;

C) p2 + 2pq + q

= 1;

D) p2 + pq + q

= 1;

E) p + 2pq + q = 1.

2. Specify an equation describing the genotypic structure of the population (multiple answers are allowed): (see

the answers to the assignment 1).

3. Specify the equation describing allelic population structure: (see answers to the assignment 1).

4. What are the conditions of validity of the law of equilibrium gene concentrations. Students were asked to

solve three problems for the application of the law of equilibrium of gene concentrations.

The results of the survey are presented in Fig. 1–3.

Fig. 1. The results of the response to the first task

Fig. 2. The results of the response to the second task

Fig. 3. The results of the response to the third task

Figure 3: The results of the response to the third task.

the genetic structure of populations over time while

meeting the requirements of technical and biological

replication. Or, in another way, consider the possi-

bilities of solving the problem of the limitations of an

educational model experiment for the study of genetic

evolutionary processes in populations.

2 TECHNIQUE AND METHODS

We consider it logical to state the essence of the de-

clared problem in the sequence of answers to the fol-

lowing questions: what is the essence of replication

in biological research? What is the essence of pseu-

doreplication in biological research, what is the his-

tory of the problem? How to ensure true replication

in a model experiment by studying complex ideal and

real biological objects in school biology (by the ex-

ample of genetic structure of the population)?

Main issue. Why should we conduct at school a

model experiment in study of the genetic structure of

the population?

Study of the issue of model experimentation with

the genetic structure of the population during 2015-

2020 convinced us that its goal is the obtention by the

students of a direct subject and mediated activity re-

sult. Subject result – 1) mastery of the essence of the

law of genetic balance and the conditions under which

it is consistent; 2) understanding of the mechanism

of inﬂuence of evolutionary factors, such as natural

selection, gene drift, gene ﬂow, mutation process on

the genetic structure of the population; understanding

of the mechanisms forming the basis of micro- and

macroevolutionary processes. The fundamental sig-

niﬁcance of the law of genetic equilibrium (Hardy-

Weinberg) is that it is the central law of population

genetics, it is based on the application of statistical

methods in genetics (Dodge, 2008).

Before developing a methodology for a model ex-

periment to study the genetic structure of a popula-

tion, we posed two auxiliary questions:

1. Is it necessary to conduct a model experiment

when studying the law of genetic equilibrium and

the conditions for its consistency?

2. Can a model experiment be replaced with other

educational methods?

The answer to the ﬁrst question is: no, not neces-

sarily. It is possible to limit to the demonstration of

the multimedia presentation and video on this topic.

The answer to the second question is: yes, it is

possible. An alternative is familiarization with the-

oretical material on a printed basis about the factors

of change in the genetic structure of a population,

overlearning of Hardy-Weinberg equations, teaching

of the solution of problems on determination of the

genetic structure of a population.

The answers to both questions demonstrate that

in the alternative version, at the best, only one result

will be achieved – a subject one. Without performing

experimental actions, it is extremely difﬁcult to form

such elements of methodological knowledge as a vari-

ant of experience, replication, sampling. In addition,

it has to be considered that the law of genetic equilib-

rium is a law, the substantial part of which consists of

abstract categories not attached to a speciﬁc biologi-

cal object (abstract homozygotes and heterozygotes,

dominant and recessive alleles, conditions for the ve-

racity of the law). And the law itself is applicable to

some really non-existent ideal object, or, conversely,

is not applicable to any really existing object (real

population).

The abovementioned reasons are the answer for us

to the main question, namely:

1) model experimentation contributes to the mastery

by the students of abstract biological categories on

concrete material objects;

The Problem of the Limitations of the Educational Model Experiment on Population Genetics and Its Solution

275

2) allows to visualize the processes in an ideal popu-

lation non-existent in reality;

3) allows to simulate the changes taking place in real

populations over several generations. Thus, for

educational purposes, the time frame of the actu-

ally occurring processes is condensed;

4) allows to vary the replications and variants of the

experiment with minimal material costs;

5) allows to teach true replicates (replications) of the

experimental impact;

6) allows to artiﬁcially quickly change the conditions

(factors) affecting the population, including acting

stochastically (Pavlotsky and Suslin, 1994).

What is the essence of replication in biological re-

search?

A person possessing a basic level of biological

knowledge within the scope of the school curriculum

of complete secondary education, the term “replica-

tion” is known as a process related to the molecu-

lar level of organization of a living being. In the

English-language scientiﬁc biological literature, the

term “replication” is used not only in the meaning of

the synthesis of new nucleotide sequences, but also in

the meaning of the replicate of experimental attempts.

In other words, the principle of replication in experi-

ment is the well-known principle of replication. The

last term is more widely used in domestic scientiﬁc

works.

Replication in biological research can be technical

and biological (Starmer, 2017).

Technical replicates give us these things:

1. They give us an accurate measurement they give

this particular object.

2. If we want to tell more about this object or we

do not want to generalize the data and transfer it

to the population - a technical experiment is what

we need.

3. They will also tell us how accurately we per-

formed the measurements.

4. “If we wanted to publish a paper about how awe-

some our new method is, we’d use technical repli-

cates” (Starmer, 2017).

5. If the experimental technique is transformed, dif-

ferent samples are taken simultaneously from one

object, then technical replication will also take

place, since they tell us about an individual.

In the biological replicates each measurement

comes from different sample that comes from differ-

ent objects.

Biological replicates give us these things:

1. Biological replicates tell us about a trait that oc-

curs in a group. In biological replicates, each

measurement comes from different samples or is

obtained differently from one object.

2. You can mix biological and technical replicates,

but the wisdom of doing this depends on the type

of the experiment. Sometimes you get more bang

for your buck if you add more biological repli-

cates and ignore technical replicates.

So, the difference between technical and biolog-

ical replication is as follows: technical replicates

are just repetition of the same experiment on the

same person.

3. Biological replicates use different biological

sources of samples (i.e. different people, different

plants, and different cell lines) (Starmer, 2017).

When choosing the type of replication of a biolog-

ical experiment, it is necessary to proceed from the

purpose in view. If it is planned to describe a speciﬁc

object, whether it be an individual, a population, or

to research a method, it is necessary to use technical

replication. If the goal is to study a group of objects,

it is necessary to choose biological replication.

What is the history of the problem of pseudorepli-

cation in biological research?

The problem of pseudoreplication was raised for

the ﬁrst time in 1984 by S. Hurlbert, who published

a critical analysis of 156 experimental scientiﬁc pa-

pers in English-language editions published in 1960–

1980s. He came to the conclusion that in 27% of

cases there was one of two variants: 1) the experi-

mental inﬂuence was applied in one replication; 2)

the experimental replications were not statistically in-

dependent. Such errors were called pseudoreplication

by S. Hurlbert. M. Kozlov notes that in Russian aca-

demic journals in 1998-2001 the part of papers based

on pseudoreplication turned out to be twice as high

(47%) than in the English-language periodicals for

1960-1980, i.e. before the publication of S. Hurlbert’s

paper. This situation was considered as non-normal,

at the same time it was pointed out that the reason for

the pseudoreplication lies not only in errors in exper-

iment planning, but also in the incorrect application

of statistical analysis to the results of a well-planned

experiment (Kozlov, 2003).

After the publication of S. Hurlbert’s paper in

1984 during the period from 1987 to 2001, accord-

ing to M. Kozlov: 1) the term “pseudoreplication”

ﬁrmly came into the ecological scientiﬁc lexicon of

foreign authors, the problem of pseudoreplication in

foreign ecological studies is actively discussed; 2) the

number of foreign publications based on pseudorepli-

cation began to decrease.

AET 2020 - Symposium on Advances in Educational Technology

276

Back in 2003, M. Kozlov paid attention to the

fact that the concept of pseudoreplication is com-

pletely unknown to the overwhelming majority of

Russian ecologists. In addition, the author empha-

sized that S. Hurlbert’s work was never cited in

Russian-language periodicals, against the background

of more than 2000 references (2015 references as of

2001) in English-language publications. M. Kozlov

repeatedly published his works on standing up for

the position that the problem of pseudoreplication is

a problem of the world scientiﬁc community, which

should be treated with all possible seriousness (Ko-

zlov and Hulbert, 2006; Kozlov, 2003).

The English term “pseudoreplication” does not

have a direct analogue in Russian, since it primarily

denotes a process – an erroneous choice of replicates

for assessment of intragroup variability in statistical

analysis (Hurlbert, 1984; Kozlov and Hulbert, 2006).

In this regard, direct translation of terminology is dif-

ﬁcult enough; the authors provide English equivalents

of key concepts. “In medical experiments, where they

are designated to as “spurious replication”, “trial in-

ﬂation”, or “the unit of analysis problem or error”

(Whiting-O’Keefe et al., 1984; Andersen, 1990; Alt-

man, Bland, 1997). Although the concept of “pseu-

doreplication”, which is most adequately translated

as “statistical analysis based on pseudoreplication”,

is not found in all works listed above, and we do not

agree with all the conclusions of the indicated authors,

all the cited studies are united by a serious approach

to the problem” (Kozlov and Hulbert, 2006).

Is pseudoreplication as scary as it might seem?

In Russian-language sources, the attitude to the

problem speciﬁed by S. Hurlbert and supported by

M. Kozlov can be characterized as far-fetched and al-

ready well-known and studied (V. Nalimov, A. Lyu-

bishchev, A. Bakanov, N. Plokhinskiy, T. Golikova).

The Russian-speaking authors agree that there are two

indisputable theses in the ideas of S. Hurlbert:

1) “it is not always correctly to extend the conclu-

sions, obtained in the study of private samplings,

to the entire general population;

2) assessment of the degree of factor inﬂuence may

turn out to be erroneous if the studied effect is

not properly localized, and the compared data

are taken from insufﬁciently randomized sources”

(Rosenberg and Gelashvili, 2008).

The conducted analysis of literary sources (Rein-

hart, 2015; Davies and Gray, 2015; Tatarnikov, 2005;

V. Veli

ckovi

c, 2007; Hurlbert, 2004; Oksanen, 2004;

Heffner et al., 1996) on the problem allowed us to sin-

gle out the “pros” and “cons” of the consideration of

the problem of pseudoreplication as signiﬁcant for bi-

ological research. The analysis results are presented

in table 1.

So, how to ensure replication in a model experi-

ment on population genetics? How to overcome the

limitations of the educational model experiment and

comply with the conditions for obtaining reliable re-

sults?

3 RESULTS

3.1 The Results of the Theoretical Stage

of the Study

The development of a model experiment methodol-

ogy aimed at the study of the essence of genetic-

evolutionary changes in the population by students,

and its improvement during 2015–2020, was carried

out by us in a staged manner. This was dictated by

the objective and subjective difﬁculties of implemen-

tation of a model experiment into teaching practice.

At the ﬁrst stage, we used only material models of

gene alleles, created models of genotypes in a manual

way, and, respectively, models of parental and daugh-

ter populations in generations. Mathematical calcula-

tions were performed without the use of a computer,

the participants in the experiment manually calculated

the frequencies of genotypes and alleles in popula-

tions, and presented the results obtained in the graph-

ical representation.

At the second stage, we combined material mod-

elling and use of the computer. Work with material

models consisted of carrying out of the experiment it-

self, creation of a model of the parental population

in manual way, and combination of the gene alle-

les at random (this is how panmixia was simulated).

The participants entered the results of the experiments

into a table on the developed web pages. With the

help of a computer, the obtained frequencies of alle-

les and genotypes were automatically calculated. In

automatic mode, the results of the experiment were

optionally presented in the graphical representation.

We have developed a web page for entering,

processing and presenting graphical view of mod-

elling results of genetic and evolutionary processes

in ideal populations, which are not inﬂuenced by

the factors of changing its genetic structure (ac-

cording to the law of Hardy-Weinberg) – http://

mybio.education/mod/exp1/en/index.html (Model ex-

periment 1. Study of the genetic structure of the ideal

population) and http://mybio.education/mod/exp2/en/

index.html (Model experiment 1. Study of the genetic

structure of the ideal population (second option)), as

well as web pages to make for entering the results of

The Problem of the Limitations of the Educational Model Experiment on Population Genetics and Its Solution

277

Table 1: Pseudoreplication – a real problem in biological research.

“Pro” arguments “Con” arguments

1. Each object in the sampling is a func-

tional part of the whole, and not a

separate element of a set. In a num-

ber of studies, the results and con-

clusions obtained for discrete objects

apply to the entire population, which

does not correspond to one of the

requirements for biological experi-

mentation – consistency in essence.

2. During the experiment, there is a

multiple determination of reaction of

the same organism in the course of

sampled counts. As an alternative,

the same sampling is studied in dif-

ferent time intervals. In this case,

living objects (their populations) are

pseudoreplications.

3. Two main problems of pseudorepli-

cation is an insufﬁcient mass nature

of experimental objects and their ini-

tial incomparability with each other.

In the ﬁrst case, the researcher re-

ceives insufﬁcient data for the con-

sistent statistical result. In the sec-

ond case, the problem has an ob-

jective causality due to the initial

uniqueness of living objects.

1. Each object in the sampling is discrete and individual.

2. Factors acting independently on the sampling, act on a set of

separate biological objects, and not on an integral object. The

speciﬁcity of a biological experiment lies in the uniqueness of

the objects and, in certain cases, in the impossibility of repeating

the experiment in an accurate manner.

3. Living objects react to the actions of factors independently on a

physical level, and thus they are statistically independent. In a

majority of research variants, living objects are true replications.

4. The speciﬁcity of living objects in their uniqueness and origi-

nality. Some ecological research involves study of the reactions

of individuals or parts to the impact. In a number of studies, it is

not possible to repeat a unique biological object, whether it be

an individual or a population.

5. The problem of pseudoreplication is artiﬁcial, since technical

and biological replication is distinguished in biology. The at-

tempt to apply the goals and requirements of technical replica-

tion to biological is a prime cause of the issue of pseudoreplica-

tion in biological experiments.

6. According to one of the points of view, the attention of English-

speaking authors to the problem of pseudoreplication is ex-

plained by several reasons:

• the desire to join the campaign of criticism and to incriminate

colleagues in pseudoreplication;

• the attempt to divert the stigma of pseudoreplication from

their work and the work of colleagues;

• as a warning signal to the reviewer that the author is ac-

quainted with the work of S. Hurlbert, therefore there should

be no comments on the paper (Rosenberg, 2019).

modelling of genetic and evolutionary processes in

populations, which are inﬂuenced by the factors of

changing its genetic structure http://mybio.education/

mod/exp3/en/index.html (Model experiment 2. Study

of the genetic structure of the population under the in-

ﬂuence of natural selection), http://mybio.education/

mod/exp4/en/index.html (Model experiment 3. Mod-

elling the effect of gene ﬂow on the genetic structure

of the population), http://mybio.education/mod/exp5/

en/index.html (Model experiment 4. Modelling the

effect of random processes on the genetic structure of

the population, modelling the drift of genes).

The system for on-line processing of modeling re-

sults developed in 2015 can be used only if the num-

ber of model individuals in the population is insignif-

icant in the model experiment. The population size is

limited by the objective possibility of creating a cor-

responding number of chip patterns of the alleles of a

gene. Optimum number of chips – 100. In this case,

the number of individuals is equal to 50. One can take

more or fewer objects. In the ﬁrst case, the choice will

be associated with the growth of material costs for the

manufacture of model elements. In the second case,

the calculated values (allele frequency) will be signif-

icantly deviate from the pre-selected frequencies, and

the level of statistical signiﬁcance of the obtained re-

sults will decrease.

Stages of modelling of the genetic structure of

populations are as following:

1. Modelling of the genetic structure of an ideal pop-

ulation with the use of material objects. Entry of

simulation results into a table on web pages http://

mybio.education/mod/exp1/en/index.html or http:

//mybio.education/mod/exp2/en/index.html.

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278

Modelling of the genetic structure of an ideal pop-

ulation can be done using the possibilities of any of

the two web pages. The difference between them lies

in the methods of processing of the experimental re-

sults, namely in the methods of calculating the fre-

quencies of genes. In the ﬁrst variant, the gene fre-

quencies are calculated automatically by the method

of extracting of the square roots of the frequencies

of the homozygotes AA and AA. In the second vari-

ant the gene frequencies are automatically calculated

according to the formulas: p = (D + 0.5H)/N, q =

(R + 0.5H)/N, where p – frequency of dominant al-

lele, q – frequency of recessive allele, D – number of

dominant homozygotes, R – number of recessive ho-

mozygotes, H – number of heterozygotes, N – total

number of members of the population. Both meth-

ods allow us to formulate the main conclusion, that

in ideal populations, the ratio of frequencies of genes

and genotypes remain constant from generation to

generation, and the sum of their frequencies is equal

to 1.

2. Modelling of population genetic structure, which

is inﬂuenced by factors of change in its genetic

structure – natural selection, gene ﬂow, genetic

drift. Entry of simulation results into a table

on web pages http://mybio.education/mod/exp3/

en/index.html, http://mybio.education/mod/exp4/

en/index.html, http://mybio.education/mod/exp5/

en/index.htmlrespectively.

Before usage of web pages for entering the results

of the simulation, high school students work with per-

sisted models of alleles of dealing a gene and create a

genetic model of the parent population. These mate-

rialized models can be checkers, chips, candies, balls

of different colours. The educational models of the

genetic structure of the population are the ﬁndings of

the experimental action with the model elements ﬁrst

ratio of genotypes and ratio of frequencies of genes,

that is, the ratio of frequencies of genotypes and genes

in the parent population.

On each of the web pages there is an in-

struction for the sequence of actions that must

be performed concerning materialized objects, as

well as actions to enter the received results in

the tables for automatic calculation of genotype

frequencies and allele frequencies. The rows that

are highlighted in blue in tables for web pages

http://mybio.education/mod/exp1/en/index.html,

http://mybio.education/mod/exp2/en/index.html,

http://mybio.education/mod/exp3/en/index.html or

http://mybio.education/mod/exp4/en/index.html,

http://mybio.education/mod/exp5/en/index.html are

ﬁlled manually by students on the basis of counting

of the number of the results obtained in the course

of the materialized models of alleles and genotypes.

The web pages provide automatic plotting of graphs

and charts, allowing, ﬁrst, to reveal the results in

graphical form (ﬁgures 4, 5). Secondly, it allows to

effectively carry out their comparative analysis and

to formulate conclusions according to the algorithm

of the action plan.

Both diagrams show the genetic structure of pop-

ulations and according to the semantic content they

are identical. They differ in the way of the visibility

of the results. The teacher can draw the students’ at-

tention to one variant of a diagram with a proposal to

compare the genetic, genotypic structure of the pop-

ulation in generations. There is another, more com-

plicated version of the analysis of the constructed di-

agrams. For this the students choose their own chart

to analyze data and formulate conclusions.

Both variants have advantages and disadvantages.

In the ﬁrst variant of the diagram, numeric data of the

results of the experiment are included in the corre-

sponding segments of each column. All the data are

displayed on the screen, so the student can quite eas-

ily compare the numbers.

In the second variant, the segments of each col-

umn are located one behind the other, and so that

the ﬁrst, the most narrow segment corresponds to the

parent generation and the last, the widest one corre-

sponds to the last child generation. This way of pre-

senting data is liked by students because, not even us-

ing numerical data it is visually easy to compare the

size (height) of colored bars. Besides, when one aims

the cursor at the corresponding ﬁeld the necessary nu-

merical information appears on the screen.

Analysis of the received data of the model exper-

imentation by the students is carried out on the basis

of the analysis of the built:

1) graphics of genetic and genotype structure of the

population in generations;

2) one of the diagrams of the genetic structure of the

population in generations;

3) graphs and diagrams that overlap.

A variety of graphic options allows to acquaint

students with the methods of their statistical process-

ing and presentation.

Testing of the developed web pages and work

on the proposed methods during 2015–2018 demon-

strated that the proposed options did not allow work-

ing with a large number of experimental objects. That

is, it was impossible to comply with the condition of

the mass scale of the experiment. In addition, the

question of the replicativity of the experiment also re-

mained open. The reasons are as follows:

The Problem of the Limitations of the Educational Model Experiment on Population Genetics and Its Solution

279

A variety of graphic options allows to acquaint students with the methods of their statistical processing and

presentation.

Fig. 4. View of graphics on the web page that were built in automatic mode http://mybio.education/mod/exp1/en/index.html

Fig. 5. View of diagrams on the web page that were built in automatic mode

Testing of the developed web pages and work on the proposed methods during 2015-2018 demonstrated that

the proposed options did not allow working with a large number of experimental objects. That is, it was impossible to

Figure 4: View of graphics on the web page that were built in automatic mode http://mybio.education/mod/exp1/en/index.

html.

1. It is physically impossible in the course of the ed-

ucational process to explore a large number of ma-

terial model objects – homozygous dominant, ho-

mozygous recessive and heterozygous individu-

als. The work was accompanied by the enormous

time spent on manual modelling and counting of

randomly formed pairs of alleles. Such a calcula-

tion had to be carried out both within one genera-

tion, and in several replications. Note that in this

variant we are talking about the difﬁculties with

the technical replication of the experiment.

2. The use of material models was limited to elemen-

tary material costs for the manufacture of model

elements. The maximum number of individuals

whose genotype models were used in the experi-

ment was equal to 50. In the case of diallelic in-

heritance of a trait (as the simplest variant of in-

heritance), the number of alleles was equal to 100.

Let’s point to the fact that in the classrooms there

were carried out parallel experiments on the study

of inﬂuence of different factors of the dynam-

ics of the population genetic structure, the work

was carried out in small groups, each of which

worked with a separate set of elements for mod-

elling. There were 5 such groups. The ﬁrst group

studied the genetic structure of an ideal popula-

tion in generations. The second group studied the

effects of gene drift. The third group studied the

essence of the gene ﬂow phenomenon. The fourth

group studied the inﬂuence of natural selection on

the genetic structure of the population. The ﬁfth

group studied the role of the mutational process in

the dynamics of the genetic structure of the popu-

lation. In total, at least a set of 500 material ele-

ments was needed for modelling.

We place the emphasis on the fact that even with

50 simulated members of the population, we obtained

results that allowed to illustrate the essence of genetic

transformations in populations in the absence of any

factors and in their presence.

In work on the improvement of the experimental

methodology, we tried to: 1) get closer in school mod-

elling of genetic-evolutionary processes to the real

process taking a course in populations; 2) take into

account signiﬁcant differences and commonality be-

tween scientiﬁc and educational experiment. Particu-

larly, this was expressed in the fact that it was neces-

sary to:

1. Cover by the experiment the maximally large

number of individuals. It has been assumed that

the hundreds and thousands of individuals could

be the experimental objects.

2. Reduce the amount of routine work for students

on the calculation of the resulting genotypes and

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280

A variety of graphic options allows to acquaint students with the methods of their statistical processing and

presentation.

Fig. 4. View of graphics on the web page that were built in automatic mode http://mybio.education/mod/exp1/en/index.html

Fig. 5. View of diagrams on the web page that were built in automatic mode

Testing of the developed web pages and work on the proposed methods during 2015-2018 demonstrated that

the proposed options did not allow working with a large number of experimental objects. That is, it was impossible to

Figure 5: View of diagrams on the web page that were built in automatic mode.

alleles in one generation.

3. Simulate a larger number of replications (repli-

cates) of the experiment, which would increase

the veracity of results and their closeness to the

mathematical formula of Hardy-Weinberg. We

also set the task to provide the possibility for tech-

nical and biological replication of an experiment

on one topic.

Thus, we set the task to provide the possibility of

technical and biological repetition of an experiment

on one topic.

Taking into account the abovementioned tasks, we

have developed a web page http://mybio.education/

mod/exp6/en/index.html (Model experiment 1. Study

of the genetic structure of the ideal population (third

variant).

Using the tools of this web page, we can con-

duct an experiment on the modelling of a structure

of an ideal population in the absence of such fac-

tors as natural selection, gene ﬂow, gene drift, mu-

tations. Note that this is the third variant for conduc-

tion of a model experiment on the stated topic. The

ﬁrst two are displayed on the following pages: http:

//mybio.education/mod/exp1/en/index.html and http:

//mybio.education/mod/exp2/en/index.html.

What is the difference between the proposed third

variant?

First. In two early variants, the number of indi-

viduals was limited by the physical ability to manu-

ally count the resulting pairs of alleles and the num-

ber of material elements for modelling. The studied

population in the proposed variant can be very large

– several hundreds, thousands, millions of individu-

als. This contributes to the implementation of the ﬁrst

of the tasks pursued by us – an increase in the num-

ber of objects used in the model experiment. And in

this case, it can be considered as a step towards the in-

crease in the veracity of the experimental results. And

thus, the maximum convergence with the actually oc-

curring genetic and evolutionary transformations in

the population. For example, for an experiment, you

can take several tens of thousands of individuals and

several million (ﬁgures 6, 7).

Second. The user (student) can independently en-

ter the initial allele frequencies in the graph for the

parental population. In the ﬁrst two variants, the al-

lele frequencies were calculated automatically after

data entering by the manual calculation of the ran-

The Problem of the Limitations of the Educational Model Experiment on Population Genetics and Its Solution

281

Fig.6 Results of a model experiment with a number of 20000 individuals, allele frequencies p (0,7) and q (0,3)

Fig.7 Results of a model experiment with a number of 2000000 individuals, allele frequencies p (0,7) and q (0,3)

Second. The user (student) can independently enter the initial allele frequencies in the graph for the parental

population. In the first two variants, the allele frequencies were calculated automatically after data entering by the

manual calculation of the randomly obtained genotypes. This function opens up an opportunity to demonstrate the

essence of biological replication of experiments. This function is especially remarkable in the lesson during the

simultaneous work of several groups of students with different populations in number and frequency of alleles

occurrence (Fig.6, Fig.8).

Figure 6: Results of a model experiment with a number of 20000 individuals, allele frequencies p (0.7) and q (0.3).

domly obtained genotypes. This function opens up an

opportunity to demonstrate the essence of biological

replication of experiments. This function is espe-

cially remarkable in the lesson during the simultane-

ous work of several groups of students with different

populations in number and frequency of alleles occur-

rence (ﬁgures 6, 8).

Third. The number of generations of the popula-

tion has been increased. In the proposed variant, it is

equal to 5. I.e. together with the parental population,

the total number of replications of the experiment is

equal to 6. In previous variants of the experiment, the

number of replications was equal to 3 (one parental

generation and two daughter generations). In addi-

tion, note that it is technically possible to increase

the number of replications by times. This will offer

an opportunity, ﬁrst of all, to quickly get a picture of

the genetic structure of the population, without both-

ering students with mechanical work on mixing and

distribution of genotypes, since there is an automatic

distribution of genotype frequencies within the lim-

its of the ideal population. Secondly, it contributes

to the implementation of one of the tasks pursued by

us – an increase in the number of replications of the

experiment within the limit of one sample (popula-

tion). This function opens an opportunity to conduct

the technical replication of experiments.

The visualized replication results are displayed on

the user’s screen by clicking the “Show graphs and di-

agrams” button. Note that in one session the user can

only see the results of technical replication, i.e. dis-

tribution of alleles and genotypes in generations with

initially speciﬁed parameters (number of individuals

and allele frequencies). The generations of the pop-

ulation will act as technical replications. In order to

simulate biological replication, it is necessary to load

the page once again without closing the previous one

and enter other initial data (the number of individuals,

allele frequencies). Within each session, generations

of a population in relation to each other will act as

technical replications, but in relation to the ﬁrst pop-

ulation and its generations – biological replications.

3.2 The Results of the Experimental

Stage of the Study

In 2019/2020 academic year, the developed web page

was tested with the participation of 6 students of the

3rd year of the Institute of Living Systems of Im-

manuel Kant Baltic Federal University, in specialty

“Biology” and 12 students of the 11th form of the

Municipal Budgetary General Education Institution

General Secondary School “School of the Future”

of Guryevsky district of Kaliningrad Region (Rus-

sian Federation). The approbation took place within

the framework of carrying out by Municipal Bud-

getary General Education Institution General Sec-

ondary School “School of the Future” together with

the National Research University Higher School of

Economics of the conference “Effective High School”

(January 23–25, 2020). Within the framework of the

conference, there were organized practical classes for

AET 2020 - Symposium on Advances in Educational Technology

282

Fig.6 Results of a model experiment with a number of 20000 individuals, allele frequencies p (0,7) and q (0,3)

Fig.7 Results of a model experiment with a number of 2000000 individuals, allele frequencies p (0,7) and q (0,3)

Second. The user (student) can independently enter the initial allele frequencies in the graph for the parental

population. In the first two variants, the allele frequencies were calculated automatically after data entering by the

manual calculation of the randomly obtained genotypes. This function opens up an opportunity to demonstrate the

essence of biological replication of experiments. This function is especially remarkable in the lesson during the

simultaneous work of several groups of students with different populations in number and frequency of alleles

occurrence (Fig.6, Fig.8).

Figure 7: Results of a model experiment with a number of 2000000 individuals, allele frequencies p (0.7) and q (0.3).

students of 11th grade on the topic “Modelling of

the genetic evolutionary processes in the population”.

One of the proposed experiments for carrying out was

a model experiment “Study of the genetic structure

of an ideal population” according to the methodology

updated by us without using material objects.

In approbation, the participants were divided into

2 groups (3 students and 6 students). One group

was asked to start with an experiment at http://mybio.

education/mod/exp1/en/index.html, and then at http:

//mybio.education/mod/exp6/en/index.html. Another

group was asked to click a link to the web page http://

mybio.education/mod/exp6/en/index.html (Model ex-

periment 1. Study of the genetic structure of the

ideal population (third variant) and simulate the ge-

netic structure of a population of any number more

than a thousand with an arbitrarily given combination

of allele frequencies. It was proposed three times to

the participants to carry out model experiment in the

third variant with different initial data (number of in-

dividuals of the population, allele frequencies). Each

of the participants of the approbation both in the ﬁrst

and second groups in carrying out of the third variant

of the experiment worked separately. The participants

were asked to use the “Show graphs and diagrams”

function, and also to formulate conclusions at the end

of the experiment.

The goals pursued by us were as follows:

1. To ﬁnd out the availability of understanding by

users of the tasks and results of experiments.

2. To ﬁnd out the main difﬁculties faced by users

when working with a web page http://mybio.

education/mod/exp6/en/index.html.

During the oral survey of the participants in the

experiment, it was found:

1. Participants of the ﬁrst group, when conducting

an experiment with material objects at the begin-

ning of work, hardly understood the essence of the

performed similar actions. Only after data enter-

ing into the table, calculation of the frequencies

of alleles and genotypes, the understanding of the

meaning of the uniformity of actions came.

2. Participants of the ﬁrst group complained about

the routine of the performed actions, increased

fatigue during their performance. Participants

sought to complete the experiment more quickly,

which increased the error rate in calculation of the

absolute number of genotypes. The latter was dis-

played at the frequency of genotypes calculated

by the program. Thus, the obtained results in sev-

eral cases were erroneous, the experimental ac-

tions had to be performed over again.

3. Participants of the ﬁrst group, after passage to the

second experiment, which, in fact, duplicated the

ﬁrst variant, but did not require manual counting,

expressed great approval of the possibility to op-

erate only with numbers.

4. Participants of the second group completed the

assigned task more quickly. However, in both

groups, there arose questions about the purpose of

three-time replicate of the experiment (with dif-

The Problem of the Limitations of the Educational Model Experiment on Population Genetics and Its Solution

283

Fig.8 Results of a model experiment with a number of 200000 individuals, allele frequencies p (0,2) and q (0,8)

Third. The number of generations of the population has been increased. In the proposed variant, it is equal to 5.

I.e. together with the parental population, the total number of replications of the experiment is equal to 6. In previous

variants of the experiment, the number of replications was equal to 3 (one parental generation and two daughter

generations). In addition, note that it is technically possible to increase the number of replications by times. This will

offer an opportunity, first of all, to quickly get a picture of the genetic structure of the population, without bothering

students with mechanical work on mixing and distribution of genotypes, since there is an automatic distribution of

genotype frequencies within the limits of the ideal population. Secondly, it contributes to the implementation of one of

the tasks pursued by us – an increase in the number of replications of the experiment within the limit of one sample

(population). This function opens an opportunity to conduct the technical replication of experiments.

The visualized replication results are displayed on the user's screen by clicking the «Show graphs and

diagrams» button. Note that in one session the user can only see the results of technical replication, i.e. distribution of

alleles and genotypes in generations with initially specified parameters (number of individuals and allele frequencies).

The generations of the population will act as technical replications. In order to simulate biological replication, it is

necessary to load the page once again without closing the previous one and enter other initial data (the number of

individuals, allele frequencies). Within each session, generations of a population in relation to each other will act as

technical replications, but in relation to the first population and its generations – biological replications.

3.2 The results of the experimental stage of the study

In 2019/2020 academic year, the developed web page was tested with the participation of 6 students of the 3

year of

the Institute of Living Systems of Immanuel Kant Baltic Federal University, in specialty «Biology» and 12 students of

the 11

form of the Municipal Budgetary General Education Institution General Secondary School «School of the

Future» of Guryevsky district of Kaliningrad Region (Russian Federation). The approbation took place within the

framework of carrying out by Municipal Budgetary General Education Institution General Secondary School «School

of the Future» together with the National Research University Higher School of Economics of the conference

«Effective High School» (January 23-25). Within the framework of the conference, there were organized practical

classes for pupils of 11

forms on the topic «Modelling of the genetic evolutionary processes in the population». One of

the proposed experiments for carrying out was a model experiment «Study of the genetic structure of an ideal

population» according to the methodology updated by us without using material objects.

In approbation, the participants were divided into 2 groups (3 students and 6 pupils). One group was asked to

start with an experiment at http://mybio.education/mod/exp1/en/index.html, and then at

http://mybio.education/mod/exp6/en/index.html. Another group was asked to click a link to the web page

http://mybio.education/mod/exp6/en/index.html (Model experiment 1. Study of the genetic structure of the ideal

population (third variant) and simulate the genetic structure of a population of any number more than a thousand with

an arbitrarily given combination of allele frequencies. It was proposed three times to the participants to carry out model

experiment in the third variant with different initial data (number of individuals of the population, allele frequencies).

Each of the participants of the approbation both in the first and second groups in carrying out of the third variant of the

Figure 8: Results of a model experiment with a number of 200000 individuals, allele frequencies p (0.2) and q (0.8).

ferent number of population and allele frequen-

cies). Note that practically no questions arose

in both groups regarding the advisability of re-

peating the experiment in generations of the same

population. It follows that the essence and neces-

sity of technical replication is recognized and ac-

cepted by the participants.

With biological replication, the situation is differ-

ent. Its objectives were not clear to the participants,

most likely due to a lack of methodological awareness

of this type of replication.

Before the performance of the experiment, we de-

liberately did not focus the participants’ attention on

the goals of repeated replicate of experimental ac-

tions. This was done in order to ﬁnd out whether the

participants understood the conditions for the verac-

ity of the results of the biological experiment. Since

among the examinees there were both students of a

biological specialty and students of graduating proﬁle

chemical and biological classes. We assumed that the

participants already possess the necessary method-

ological tools for planning, conduction of biological

experiments and interpretation of the results. The re-

sults of approbation showed that teaching the method-

ology of a biological experiment should be started

with distinguishing between technical and biological

replication of experimental effects. We can only as-

sume that a lack of understanding of the differences

between them (for purposes, methodology) could ini-

tiate the spread of the problem of pseudoreplication

in biological research in principle. We believe that

in order to conﬁrm this assumption, it is necessary

to conduct additional studies aimed at a retrospective

analysis of biological scientiﬁc literature, primarily

of scientiﬁc papers, conference materials containing

a description of the methods and results of experi-

ments. The question is, is it worth doing? Or to ac-

cept the fact that even if we consider the problem of

pseudoreplication as far-fetched, then the issue of dis-

tinguishing between technical and biological replica-

tions and teaching this in the secondary school and in

higher educational establishment deﬁnitely deserves

further study.

4 CONCLUSIONS

As a result of work on the topic of overcoming

methodological difﬁculties in conducting a model ex-

periment on population genetics, we came to the fol-

lowing conclusions:

1. Model experiment on the study of genetic-

evolutionary processes in populations by means

of computer modelling is ideal for demonstration

of the essence of technical and biological replica-

tion.

2. The use of technical and biological replication in

a model experiment makes it possible to take into

account the requirement of repetition and mass

scale of the experimental impact. This is neces-

AET 2020 - Symposium on Advances in Educational Technology

284

sary to obtain reliable results.

3. In the educational model experiment, it is impos-

sible to take into account all the requirements for

a scientiﬁc biological experiment, therefore, it is

necessary to rely only on its essential features.

5 OUTLOOK

Further work on studying the possibilities of a model

experiment in training of the students of 11 grade and

students-biologists in true replication, as well as the

essence of technical and biological replication, we

can see in the following. It is necessary to develop and

approbate web pages to model the structure of a very

large population under the inﬂuence on its numerous

generations of such factors as natural selection, gene

ﬂow, gene drift, mutations.

The modelling of the genetic structure should

be fully automated. The initial platforms for

improvement of methodology will be the exist-

ing web pages http://mybio.education/mod/exp3/en/

index.html (Model experiment 2. Study of the genetic

structure of the population under the inﬂuence of nat-

ural selection), http://mybio.education/mod/exp4/en/

index.html (Model experiment 3. Modelling the ef-

fect of gene ﬂow on the genetic structure of the pop-

ulation), http://mybio.education/mod/exp5/en/index.

html (Model experiment 4. Modelling the effect of

random processes on the genetic structure of the pop-

ulation, modelling the drift of genes

∗

), providing one

of the stages of work with material objects.

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